Graphene has demonstrated extraordinary electrical, optical, thermal and mechanical properties. In last decade, a lot of research has been done to improve fabrication and solution processing of graphene to graphene oxide and reduced graphene oxide. Graphene oxide contains more number of oxygen containing functional groups which increase interlayer distance and make its dispersion easy in aqueous solutions. These advances in graphene have further improved its properties including tensile strength, elastic modulus, low resistance, carrier mobility and stability against higher temperatures and chemicals. Alginate is obtained from brown seaweeds and has potential applications in treatment of wounds and cell differentiation due to its non-toxicity, biodegradability and biocompatibility. It is a hydrophilic natural polysaccharide and provides moist and ideal environment for wound healing and cell growth. However, Alginate fibers still also display some unsatisfactory properties, such as low mechanical strength and electrical conductivity. Combining the intriguing properties of graphene and alginate, we develop smart composite fibers with suitable conductivity and mechanical strength which can be processed to nonwoven wound dressings and can be used as biosensors for medical applications. Sodium alginate/Graphene oxide fibers were fabricated by using wet spinning setup. The developed sodium alginate/graphene oxide fibers were further thermally and chemically reduced to improve conductivity. Their structure and properties were characterized by conductivity measurements, fiber strength testing, absorption behaviors, FTIR (Fourier transform infrared spectroscopy) and SEM (scanning electron microscope). The addition of graphene oxide improves the strength of sodium alginate/graphene oxide fibers due to high compatibility and even distribution of graphene oxide fillers in alginate matrix. Thermal and chemical reduction methods increase the conductivity of sodium alginate/graphene oxide fibers due to removal of oxygen containing groups. Chemical reduction method seems to have greater effect in improving the conductive properties of sodium alginate/graphene oxide fibers. These fibers also have good ability to absorb fluid and forms hydrogel to keep appropriate moist environment for wound healing which make them ideal material to develop smart wound dressings.